A. Y. Aydemir

Nonlinear studies of m = 1 modes in high-temperature plasmas

Nonlinear evolution of the m=1 mode is examined in high‐temperature plasmas where the mode is in the semicollisional or collisionless regime. Unlike the finite −Δ’(m≥2) tearing modes, the nonlinear evolution of which is collisional, both the semicollisional and collisionless m=1 modes exhibit nonlinearly enhanced growth rates that far exceed their linear values, thus making their nonlinear evolution collisionless; this accelerated growth of a collisionless m=1 mode may explain the fast sawtooth crashes observed in large tokamaks.

Stabilization of the resistive shell mode in tokamaks

The stability of current-driven external-kink modes is investigated in a tokamak plasma surrounded by an external shell of finite electrical conductivity. According to conventional theory, the ideal mode can be stabilized by placing the shell sufficiently close to the plasma, but the non-rotating `resistive shell mode`, which grows as the characteristic L/R time of the shell, always persists. It is demonstrated, using both analytic and numerical techniques, that a combination of strong edge plasma rotation and dissipation somewhere inside the plasma is capable of stabilizing the resistive shell mode. This stabilization mechanism is similar to that found recently by Bondeson and Ward (1994), except that it does not necessarily depend on toroidicity, plasma compressibility or the presence of resonant surfaces inside the plasma. The general requirements for the stabilization of the resistive shell mode are elucidated

A unified Monte Carlo interpretation of particle simulations and applications to non‐neutral plasmas

Using a ‘‘Monte Carlo interpretation’’ of particle simulations, a general description of low‐noise techniques, such as the δf method, is developed in terms well‐known Monte Carlo variance reduction methods. Some of these techniques then are applied to linear and nonlinear studies of pure electron plasmas in cylindrical geometry, with emphasis on the generation and nonlinear evolution of electron vortices. Long‐lived l=1 and l=2 vortices, and others produced by unstable diocotron modes in hollow profiles, are studied. It is shown that low‐noise techniques make it possible to follow the linear evolution and saturation of even the very weakly unstable resonant diocotron modes.

Electron thermal confinement studies with applied resonant fields on TEXT

Externally applied magnetic fields are used on the Texas Experimental Tokamak (TEXT) to study the possibility of controlling the particle, impurity and heat fluxes at the plasma edge. Fields with toroidal mode number n = 2 or 3 and multiple poloidal mode numbers m (dominantly m = 7) are used, with a poloidally and toroidally averaged ratio of radial to toroidal field components 〈|br/Bo〉 ≅0. 1%. Calculations show that it is possible to produce mixed islands and stochastic regions at the plasma edge (r/a ≥ 0.8) without affecting the interior. The expected magnetic field structure is described and experimental evidence of the existence of this structure is presented. The edge electron temperature decreases with increasing 〈|br/Bo〉, while interior values are not significantly affected. The implied increase in edge electron thermal diffusivity is compared with theoretical expectations and is shown to agree with applicable theories to within a factor of three.

Convective transport in the scrape-off layer of tokamaks

A detailed study of blob formation, dynamics, and the associated convective transport in the scrape-off layer (SOL) of tokamak plasmas is presented. Dissipation level in the system, in addition to the blob size, is shown to play an important role in determining whether a blob propagates as a coherent object. Nonlinear SOL interchange/ballooning modes are shown to be capable of creating blobs near the separatrix without relying on the core or edge-plasma dynamics. Finally, the SOL density profiles under diffusive and convective transport assumptions are compared. In the convective regime, here assumed to be driven by the SOL interchange modes, two different scaling with the machine size R is found for the characteristic density “e-folding” length λn. When the dominant loss mechanism for the blobs is diffusive, the scale length becomes independent of machine size as the connection length increases. In the less typical case where the parallel losses along the open field lines dominate, λn∼R1∕2.

Magnetohydrodynamic modes driven by anomalous electron viscosity and their role in fast sawtooth crashes

Dispersion relations are derived for both small‐ and large‐Δ’ modes (m≥2 and m=1 modes, respectively) driven by anomalous electron viscosity. Under the assumption that the anomalous kinematic electron viscosity is comparable to the anomalous electron thermal diffusivity, it is found that the viscous mode typically has a higher growth rate than the corresponding resistive mode. Computational results in cylindrical and toroidal geometries are compared with theory and some nonlinear results for viscous m=1 modes in both circular and D‐shaped boundaries are presented and their possible role in fast sawtooth crashes is discussed.

Toroidal studies of sawtooth oscillations in tokamaks

Tokamak sawtooth oscillations are studied with a nonreduced, fully toroidal, resistive magnetohydrodynamic (MHD) model that includes Ohmic heating, and parallel and perpendicular thermal conductions. Effects of perpendicular transport in producing different types of sawteeth, varying from simple, periodic oscillations to giant sawteeth with temperature modulations of order unity, and compound sawteeth with multiple relaxations, are demonstrated. Some of the recent experimental observations from large tokamaks, such as the fast crash times and a presumed topological anomaly in the x‐ray tomography pictures, thought to be inconsistent with the Kadomtsev reconnection model, are examined and possible explanations are offered.

Linear studies of m=1 modes in high-temperature plasmas with a four-field model

The m=1 mode in high temperature plasmas is examined using a simple four‐field model of tokamak dynamics derived by Hazeltine et al. [Phys. Fluids 30, 3204 (1987)]. It is shown that, despite its simplicity, the model reproduces with remarkable accuracy results obtained with more sophisticated kinetic treatments in various collisionality regimes. The effects of parallel compressibility on the m=1 mode in the collisional, semicollisional, and collisionless regimes are also discussed. Coupling to the ion sound waves is found to be weakly destabilizing in the collisional regime, and stabilizing in the semicollisional and collisionless regimes.

Collisionless electron heating in inductively coupled discharges

A kinetic theory of collisionless electron heating is developed for inductively coupled discharges with a finite length L. The novel effect associated with the finite-length system is the resonance between the bounce motion of the electrons and the wave frequency, leading to enhanced heating. The theory is in agreement with results of electromagnetic particle simulations.

Shear flows at the tokamak edge and their interaction with edge-localized modes

Shear flows in the scrape-off layer (SOL) and the edge pedestal region of tokamaks are shown to arise naturally out of transport processes in a magnetohydrodynamic model. In quasi-steady-state conditions, collisional resistivity coupled with a simple bootstrap current model necessarily leads to poloidal and toroidal flows, mainly localized to the edge and SOL. The role of these flows in the grad-B drift direction dependence of the power threshold for the L (low) to H (high) transition, and their effect on core rotation, are discussed. Theoretical predictions based on symmetries of the underlying equations, coupled with computational results, are found to be in agreement with observations in Alcator C-Mod [Phys. Plasmas 12, 056111 (2005)]. The effects of these self-consistent flows on linear peeling/ballooning modes and their nonlinear consequences are also examined.